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<title>Problem 1586. -- 路径统计path -- 衡阳八中OJ离线版-2012-02-29</title><center><h2>1586: 路径统计path</h2><span class=green>Time Limit: </span>5 Sec&nbsp;&nbsp;<span class=green>Memory Limit: </span>162 MB<br><span class=green>Submit: </span>30&nbsp;&nbsp;<span class=green>Solved: </span>18<br>[<a href='submitpage.php?id=1586'>Submit</a>][<a href='problemstatus.php?id=1586'>Status</a>][<a href='bbs.php?id=1586'>Discuss</a>]</center><h2>Description</h2><div class=content>
	
一个矩阵由r行c列共r*c个小正方形组成。行从下到上编号为1到r，列从左到右编号为1到c。所有坐标都是(row,colmn)的形式。
给出n个特殊点的坐标，保证特殊点在矩阵内，依次编号为1到n，从(1,1)到(r,c)的包含严格k个特殊点的路径称为k型路径。
同时路径必须遵循以下规则：
1.	每次你只能向上或向右。即你只能从(x,y)走到(x+1,y)或(x,y+1)
2.	特殊点在路径中出现的顺序必须与给出的顺序相同，即如果特殊点a出现在特殊点b之前，那么a必须小于b。
请输出0型路径，1型路径…,n型路径的条数mod 1000007
</div><h2>Input</h2><div class=content>第一行两个数R,C。
第二行描述1-n号特殊点的行号。请读到行尾。
第二行描述1-n号特殊点的列号。

</div><h2>Output</h2><div class=content>N+1个用空格隔开的整数，分别表示1型路径…,n型路径的条数mod 1000007

</div><h2>Sample Input</h2>
			<div class=content><span class=sampledata>3<br />
3<br />
2 3<br />
2 2<br />
<br />
</span></div><h2>Sample Output</h2>
			<div class=content><span class=sampledata>1 3 2<br />
<br />
【样例解释】<br />
0型路径<br />
(1, 1) -> (1, 2) -> (1, 3) -> (2, 3) -> (3, 3)<br />
1型路径<br />
(1, 1) -> (2, 1) -> (2, 2) -> (2, 3) -> (3, 3)<br />
(1, 1) -> (1, 2) -> (2, 2) -> (2, 3) -> (3, 3)<br />
(1, 1) -> (2, 1) -> (3, 1) -> (3, 2) -> (3, 3)<br />
2型路径<br />
(1, 1) -> (2, 1) -> (2, 2) -> (3, 2) -> (3, 3)<br />
(1, 1) -> (1, 2) -> (2, 2) -> (3, 2) -> (3, 3)<br />
<br />
【数据规模】<br />
对于100%数据<br />
1<=R,C<=50<br />
0<=N<=50<br />
</span></div><h2>HINT</h2>
			<div class=content><p></p></div><h2>Source</h2>
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